1. Location Case Study Shanghai GM Service Parts Part II
John H. Vande Vate
Spring 2006 1

2. Schedule Driven Transport
Service a primary driver
Product has relatively high value
The transportation network is likely Schedule Driven, (e.g. daily deliveries)
Alternative is Load Driven (deliver whenever there’s enough demand for a full truckload)
For now, let’s assume 5 days a week 2

3. Cost of Transportation
Mileage
Number of lanes
So?! 3

4. Where the parts come from4

5. Where they go… 5

6. Assumptions Schedule, not capacity drives transport
Handling fees are “nominal” … 6

7. Inventory Consolidation should Assumption: Have no effect
On inventory at supplier
On inventory at dealerships
Create some inventory at the DCs
Add to pipeline inventory
Assumption:
Each lane creates inventory equal to half the value of its average shipment 7

8. Consequences Inventory depends on the lanes not just the number of DCs
Trade-offs are
Capital cost of DCs &
Additional inventory at DCs vs
Savings in Freight Consolidation
We are ignoring pipeline effects as they are probably small. 8

9. Mechanical Consequences
The ALT Heuristic now has
Flow problem: Determine how goods move from suppliers to dealers (e.g., what do we run through DCs)
Location problem: Determine where to put the DCs
Comment: This is still a heuristic and by no means the only possibility.
An MIP
Convex Opt. 9

10. The Flow Problem Multi-Commodity Network Flow
Supply (Scaled to weekly value)
Supplies from each province are a commodity, e.g., supplies from Heilongjiang
Demand (Scaled to weekly value)
Assume demand is the same everywhere (i.e., 1% of the value of parts comes from Heilongjiang so 1% of the value of demand for parts in each province is for parts from Heilongjiang.)
The Network
Supply Provinces direct to Dealers
Supply Provinces to DCs
DCs to DCs
DCs to dealers 10

11. The Cost Structure Consolidate!
If you send flow (of any product) from one location to another,
you pay for daily shipments
you create inventory at the destination
Note the transportation costs does NOT depend on how much flow you send, just whether you send any at all, so….
Consolidate! 11

12. Inventory Cost
Pay inventory carrying cost of ½ the value of average shipment on each lane
WEEKLY holding rate
e.g., = 20%/50 weeks
Value of average shipment of product
Flow[fromnode, tonode, product]/5
Value of a weeks shipments
Number of shipments/week 12

13. Do we ship that way or not
Modeling the Cost
Model the flows
Flow[fromnode, tonode, product] is how much of a given “product” we send directly from “fromnode” to “tonode”
UseLane[fromnode, tonode] is the BINARY variable indicating whether or not we send flow of any product from “fromnode” to “tonode”
Cost: To get weekly transport cost
5*CostPerMile*Distance*UseLane
Add those up across all the lanes
Cost of each shipment
Do we ship that way or not
Shipments per week 13

14. Don’t Forget Constraints to ensure the meaning
Method #1: For each (fromnode, tonode)
BigEnoughNumber*UseLane[fromnode, tonode] >=
sum{(fromnode, tonode) in EDGES, product in PRODUCTS}
Flow[fromnode, tonode, product];
Method #2: For each (fromnode, tonode, product)
Supply[product]*UseLane[fromnode, tonode] >=
Which is better? 14

15. Caution Fixed Charge Network Flow Problem Typically difficult to solve
LP Relaxation is far from the MIP
CPLEX adds cuts to close this gap
These are constraints implied by the integer variables 15

16. This changes as we move the DCs
Re-Locating The DC’s
Just like before
Fix the transportation network and change the locations of the dcs
5*CostPerMile*Distance*UseLane
This changes as we move the DCs
This is fixed for now 16

17. Need that to balance inventory and transport
The Data
Read the Supplier Locations and %’s
Read the Province Locations and %’s
Read the current DC locations and whether they are open
Some additional parameters
param CostPerMile default 2;
param HoldingRate default 0.004;
param WeeklyVolume default ;
Need that to balance inventory and transport 17

18. The Model & Script 18

19. Running the Model 19

20. The Solution 20

21. The Solution 21

22. Advantages Equipment Balance
Vehicles cycling among the DCs
Vehicles traveling back and forth between
Supplier Province and DC
Single Sourcing (even though we didn’t insist on it) 22

23. What should we consider next?
Every day?! It’s a 7 day trip 23

24. Frequency! Add a set of FREQUENCIES Expanded the variables
E.g., 1, 3, or 5 times per week
Expanded the variables
UseLane[fromnode, tonode, frequency]
That let’s us capture the cost:
Frequency*Distance*UseLane…
Flow[fromnode, tonode, product, frequency]
That let’s us capture inventory
HoldingRate*Flow [fromnode, tonode, product, frequency]/(2*frequency) 24

25. Some Comments
You have to conserve product at a DC, but you don’t have to conserve frequency
Product from Heilongjiang comes in weekly, but goes out daily
Our estimate of inventory is pretty rough at the DCs but it’s good at the Provinces
3 Frequency options mean the model is 3X as large….that really slows things down. 25

26. Where’s to Use Frequency
There are also other reasons for high frequency
Shanghai
Blue 5
Guangzhou
Pink
Hangzhou
Nanjing
Red
Jinan 3
Beijing
Shijiazhuang 26

27. What Next? Geographic Details Transportation Cost Details
Provincial demand not all centered on the capital.
The split to DCs may not match the assignment of the capitals
Transportation Cost Details
May be savings from round trips
May have capacity issues on some lanes …
What’s happening to the effort?
What’s happening to the impact? 27

28. What’s Next For Us? No Class February 21st
Review for the exam
Work on your projects
In Class Exam on February 23rd
Covers lectures through today
Open-book, open-notes
YOUR OWN WORK 28

29. Modeling Questions Two kinds of answers possible
Unambiguous AMPL-like formation
Excel formulation (less preferred but acceptable)
See the example 29

30. After the Exam BMW Case Study Do not miss this Modeling Variability
Impact of Improved Forecasting
Impact of Increased Frequency
Managing Variability in Supply
Do not miss this 30